Signal Temporal Logic Specification Research Articles

Dynamic event‐triggered prescribed performance control for nonlinear systems with signal temporal logic

AbstractThis article is concerned with the problem of dynamic event‐triggered prescribed performance control for nonlinear systems under signal temporal logic tasks. By utilizing the method of prescribed performance control, the constrained plant can be transformed into an unconstrained one, and a dynamic event‐triggered feedback control law is generated for the transformed system to ensure that the signal temporal logic specification is satisfied. A dynamic event‐triggered mechanism is designed to guarantee the event‐triggered stability, safety and complex specification. Besides, Zeno phenomenon is definitely avoided. Compared with the continuous‐time feedback controller, the event‐triggered controller has proven to be effective in reducing sensing, communication and computation costs. Finally, two simulations are given to illustrate the effectiveness of theoretical results.

Backpropagation through signal temporal logic specifications: Infusing logical structure into gradient-based methods

This paper presents a technique, named STLCG, to compute the quantitative semantics of Signal Temporal Logic (STL) formulas using computation graphs. STLCG provides a platform which enables the incorporation of logical specifications into robotics problems that benefit from gradient-based solutions. Specifically, STL is a powerful and expressive formal language that can specify spatial and temporal properties of signals generated by both continuous and hybrid systems. The quantitative semantics of STL provide a robustness metric, that is, how much a signal satisfies or violates an STL specification. In this work, we devise a systematic methodology for translating STL robustness formulas into computation graphs. With this representation, and by leveraging off-the-shelf automatic differentiation tools, we are able to efficiently backpropagate through STL robustness formulas and hence enable a natural and easy-to-use integration of STL specifications with many gradient-based approaches used in robotics. Through a number of examples stemming from various robotics applications, we demonstrate that STLCG is versatile, computationally efficient, and capable of incorporating human-domain knowledge into the problem formulation.

STL2vec: Signal Temporal Logic Embeddings for Control Synthesis With Recurrent Neural Networks

In this letter, a method for learning a recurrent neural network (RNN) controller that maximizes the robustness of signal temporal logic (STL) specifications is presented. In contrast to previous methods, we consider synthesizing the RNN controller for which the user is able to select an STL specification arbitrarily from multiple STL specifications. To obtain such a controller, we propose a novel notion called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">STL2vec</i> , which represents a vector representation of the STL specifications and exhibits their similarities. The construction of the STL2vec is useful since it allows us to enhance the efficiency and performance of the controller. We validate our proposed method through the examples of the path planning problem.

Mining Road Traffic Rules with Signal Temporal Logic and Grammar-Based Genetic Programming

Traffic systems, where human and autonomous drivers interact, are a very relevant instance of complex systems and produce behaviors that can be regarded as trajectories over time. Their monitoring can be achieved by means of carefully stated properties describing the expected behavior. Such properties can be expressed using Signal Temporal Logic (STL), a specification language for expressing temporal properties in a formal and human-readable way. However, manually authoring these properties is a hard task, since it requires mastering the language and knowing the system to be monitored. Moreover, in practical cases, the expected behavior is not known, but it has instead to be inferred from a set of trajectories obtained by observing the system. Often, those trajectories come devoid of human-assigned labels that can be used as an indication of compliance with expected behavior. As an alternative to manual authoring, automatic mining of STL specifications from unlabeled trajectories would enable the monitoring of autonomous agents without sacrificing human-readability. In this work, we propose a grammar-based evolutionary computation approach for mining the structure and the parameters of an STL specification from a set of unlabeled trajectories. We experimentally assess our approach on a real-world road traffic dataset consisting of thousands of vehicle trajectories. We show that our approach is effective at mining STL specifications that model the system at hand and are interpretable for humans. To the best of our knowledge, this is the first such study on a set of unlabeled real-world road traffic data. Being able to mine interpretable specifications from this kind of data may improve traffic safety, because mined specifications may be helpful for monitoring traffic and planning safety promotion strategies.

Planning of Heterogeneous Multi-Agent Systems Under Signal Temporal Logic Specifications With Integral Predicates

We address the problem of coordinating the trajectories of heterogeneous multi-agent systems under spatio-temporal specifications. In particular, we consider global Signal Temporal Logic (STL) constraints to express the number and type of agents that should be present at specific locations within the desired time windows. We also introduce an integral predicate to specify cumulative progress that can be achieved asynchronously by multiple agents. In order to generate optimal trajectories, we formulate a mixed-integer linear program whose objective is minimizing the agent movement subject to the heterogeneous abstracted dynamics of the agents and a global STL specification including the novel integral predicate. We demonstrate the performance of the proposed method via simulations and experiments with drones.

Extending Signal Temporal Logic with Quantitative Semantics by Intervals for Robust Monitoring of Cyber-physical Systems

Monitoring is the core procedure of runtime verification of cyber-physical systems (CPS) and provides an evaluation of a signal with respect to a given specification. For formally specifying requirements with time constraints for CPS, Signal Temporal Logic (STL) is a well-known specification language with powerful semantics. However, with existing semantics of STL it is not feasible to monitor signals with spatial deviation and time delay. Therefore, we introduce STL with Quantitative Interval Semantics to solve this problem. Based on this newly developed semantics, we derived an algorithm called RoMoTeS (Robust Monitoring for Temporal Specifications) to monitor a signal with finite length with respect to an STL formula. It provides a real-valued interval for every point in time, which contains all possible signed distances between the deviation polytope determined by the measured data point (exposed to deviation and delay) and the permissive space specified by an STL specification. Furthermore, it is proven that no satisfaction is reported when the signal is potentially falsifying such a specification. Finally, an automatic transmission controller model was used as a case study to show the applicability and usefulness of the proposed algorithm.

Worst-case Satisfaction of STL Specifications Using Feedforward Neural Network Controllers

In this paper, a reinforcement learning approach for designing feedback neural network controllers for nonlinear systems is proposed. Given a Signal Temporal Logic (STL) specification which needs to be satisfied by the system over a set of initial conditions, the neural network parameters are tuned in order to maximize the satisfaction of the STL formula. The framework is based on a max-min formulation of the robustness of the STL formula. The maximization is solved through a Lagrange multipliers method, while the minimization corresponds to a falsification problem. We present our results on a vehicle and a quadrotor model and demonstrate that our approach reduces the training time more than 50 percent compared to the baseline approach.

Shrinking Horizon Model Predictive Control With Signal Temporal Logic Constraints Under Stochastic Disturbances

We present shrinking horizon model predictive control for discrete-time linear systems under stochastic disturbances with constraints encoded as signal temporal logic (STL) specification. The control objective is to satisfy a given STL specification with high probability against stochastic uncertainties while maximizing the robust satisfaction of an STL specification with minimum control effort. We formulate a general solution, which does not require precise knowledge of probability distributions of (possibly dependent) stochastic disturbances; only the bounded support of the density functions and moment intervals are used. For the specific case of disturbances that are normally distributed, we optimize the controllers by utilizing knowledge of the probability distribution of the disturbance. We show that in both cases, the control law can be obtained by solving optimization problems with linear constraints at each step. We experimentally demonstrate effectiveness of this approach by synthesizing a controller for a heating, ventilation, and air conditioning system.

Monitoring properties of analog and mixed-signal circuits

In this paper, we present a comprehensive overview of the property-based monitoring framework for analog and mixed-signal systems. Our monitoring approach is centered around the Signal Temporal Logic (Stl) specification language, and is implemented in a stand-alone monitoring tool (Amt). We apply this property-based methodology to two industrial case studies and briefly present some recent extensions of Stl that were motivated by practical needs of analog designers.